Synthese 179 (3):435 - 454 (2011)
This paper considers the nature and role of axioms from the point of view of the current debates about the status of category theory and, in particular, in relation to the "algebraic" approach to mathematical structuralism. My aim is to show that category theory has as much to say about an algebraic consideration of meta-mathematical analyses of logical structure as it does about mathematical analyses of mathematical structure, without either requiring an assertory mathematical or meta-mathematical background theory as a "foundation", or turning meta-mathematical analyses of logical concepts into "philosophical" ones. Thus, we can use category theory to frame an interpretation of mathematics according to which we can be structuralists all the way down
|Keywords||Mathematical structuralism Category theory Algebraic structuralism Philosophy of mathematics Hilbert Frege Shapiro McLarty Marquis Hellman Mac Lane|
|Categories||categorize this paper)|
References found in this work BETA
Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 1997 - Oxford University Press.
Foundations Without Foundationalism: A Case for Second-Order Logic.Stewart Shapiro - 1991 - Oxford University Press.
An Answer to Hellman's Question: ‘Does Category Theory Provide a Framework for Mathematical Structuralism?’.Steve Awodey - 2004 - Philosophia Mathematica 12 (1):54-64.
From Kant to Hilbert: A Source Book in the Foundations of Mathematics.William Bragg Ewald (ed.) - 1996 - Oxford University Press.
Introduction to Higher Order Categorical Logic.J. Lambek & P. J. Scott - 1989 - Journal of Symbolic Logic 54 (3):1113-1114.
Citations of this work BETA
Towards a Unified Framework for Decomposability of Processes.Valtteri Lahtinen & Antti Stenvall - forthcoming - Synthese:1-17.
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